Level-crossing, theory

Note that the position of the juLCR depends on the sign of the nuclear hyperfine parameter relative to that of the muon. Using degenerate perturbation theory one can calculate the effects of the level crossing on the... 

This level of theory outhned above is implemented in the ENDyne code [18]. The explicit time dependence of the electronic and nuclear dynamics permits illustrative animated representations of trajectories and of the evolution of molecular properties. These animations reveal reaction mechanisms and details of dynamics otherwise difficult to discern, making the approach particularly suitable for the study of the subtleties of contributions to the stopping cross section. 

Figure 4- Left Density of states (DOS) of cage-like and amorphous structures of Au clusters with 18 and 20 atoms, calculated at the LDA and GGA levels of theory. Right Total energy difference between cage-like and compact equilibrium structures of cationic, neutral, and anionic clusters with 18 (starts), 20 (crosses), and 32 (circles) atoms.

Like N4, cubic Ng is expected to have a substantial dissociation barrier since the orbital correlation of Ns with 4N2 shows a crossing of occupied and unoccupied orbitals [4], Recent theoretical studies [3,60-63] have confirmed that the energy barrier for dissociation into N2 molecules is predicted to be 10-22 kcal/mol depending on the level of theory, and the pathway is likely to be a stepwise dissociation reaction such as Ng - N2 +... 

Fig. 3. Optimized geometries of stationary points on the N4 triplet potential energy surface. Note that 6 is not a stationary point at higher levels of theory, and 7S-T is the minimum crossing point between the 1A and the " surfaces.

The main difference between the new potential and that of Buck et al., i.e. the depth of potential wells, cannot be verified by this high energy scattering calculation in order to provide major insights, work is in progress to compute the MO-VB PES at a higher level of theory and to calculate differential cross-sections at the lower collision energy of 275 cm 1 [69], where total inelastic and some state resolved differential cross sections are available [65]. 

In the present study, optimizations of minima, transition states, PEH crossings, and minimum energy paths (MEPs) have been here performed initially at the CASSCF level of theory for all reported systems [2], MEPs have been built as steepest descendent paths in a procedure [ 10] which is based on a modification of the... 

With the constraints of Eq. 47 we can, in general, use perturbation theory to find the approximate eigenvalues oiT-Lp. In the coming sections we will do so by using van Vleck perturbation theory, but only after discussing Floquet energy level crossings. 

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